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Simulations, Data Analysis and Algorithms

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Table 8 Initial states left (L) and right (R) for the Riemann problems for the Baer-Nunziato equations

From: Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

  \(\boldsymbol{\rho}_{\boldsymbol{s}}\) \(\boldsymbol{u}_{\boldsymbol{s}}\) \(\boldsymbol{p}_{\boldsymbol{s}}\) \(\boldsymbol{\rho}_{\boldsymbol{g}}\) \(\boldsymbol{u}_{\boldsymbol{g}}\) \(\boldsymbol{p}_{\boldsymbol{g}}\) \(\boldsymbol{\phi}_{\boldsymbol{s}}\) \(\boldsymbol{t}_{\boldsymbol{e}}\)
BNRP1 (Deledicque and Papalexandris 2007): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L 1.0 0.0 1.0 0.5 0.0 1.0 0.4 0.10
R 2.0 0.0 2.0 1.5 0.0 2.0 0.8  
BNRP2 (Deledicque and Papalexandris 2007): \(\gamma_{s} = 3.0\), \(\pi_{s} = 100\), \(\gamma_{g} = 1.4\), \(\pi_{g} = 0\)
L 800.0 0.0 500.0 1.5 0.0 2.0 0.4 0.10
R 1,000.0 0.0 600.0 1.0 0.0 1.0 0.3  
BNRP3 (Deledicque and Papalexandris 2007): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L 1.0 0.9 2.5 1.0 0.0 1.0 0.9 0.10
R 1.0 0.0 1.0 1.2 1.0 2.0 0.2  
BNRP5 (Schwendeman et al. 2006): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L 1.0 0.0 1.0 0.2 0.0 0.3 0.8 0.20
R 1.0 0.0 1.0 1.0 0.0 1.0 0.3  
BNRP6 (Andrianov and Warnecke 2004): \(\gamma_{s} = 1.4\), \(\pi_{s} = 0\), \(\gamma _{g} = 1.4\), \(\pi_{g} = 0\)
L 0.2068 1.4166 0.0416 0.5806 1.5833 1.375 0.1 0.10
R 2.2263 0.9366 6.0 0.4890 −0.70138 0.986 0.2  
  1. Values for \(\gamma_{i}\), \(\pi_{i}\) and the final time \(t_{e}\) are also reported.